: Lorentz transformation Equation in Modern Physics.

Abstract

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with as chosen x- or y-axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is not aligned with either the x- or the y-axis. In this paper we develop these transformations and show that under such transformations, two orthogonal systems (in their respective frames) appear non-orthogonal to each other. We also illustrated the usefulness of the transformation by applying it to three problems including the rod-slot problem. We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einsteins distant clocks synchronization procedure